Thermal noise presents a fundamental limit to measurement sensitivity in diverse areas of science and technology. One particularly important setting is that of optical interferometry in which otherwise stable structures experience small, thermally driven fluctuations in their dimensions that lead to performance limitations in applications ranging from laser spectroscopy and frequency metrology [1, 2], to the detection of gravitational waves [3], and to the realization of quantum behavior for macroscopic objects. [1] K. Numata, M. Ando, K. Yamanloto, S. Otsuka, and K. Tsubono, Phys. Rev. Lett. 91, 260602 (2003), the entire content of which is incorporated herein by reference.[2] K. Numata, A. Kemery, and J. Camp, Phys. Rev. Lett. 93, 250602 (2004), the entire content of which is incorporated herein by reference.[3]V. B. Braginsky, M. L. Gorodetsky, and S. P. Vyatchanin, Phys. Lett. A 264, 1 (1999), the entire content of which is incorporated herein by reference.
For definiteness, consider a Fabry-Perot resonator formed by the reflective surfaces of two mirrors that are either freely suspended (e.g., one arm of a gravitational wave interferometer) or separated by a rigid spacer (e.g., laser stabilization for an optical atomic clock). Over frequency regimes of practical importance for such interferometers, the dominant limitation to length stability often originates from thermally driven displacement noise for the reflective surfaces of the mirror substrates, and not from the supporting structure [2]. The fluctuations of the mirror surfaces are of fundamental origin and arise from small, dissipative components of the elastic constants of the mirror and substrate materials as demanded by the Fluctuation-Dissipation Theorem [4, 5, 6]. As discussed above, these thermally driven fluctuations lead to performance limitations in applications ranging from laser spectroscopy and frequency metrology, to the detection of gravitational waves, and to the realization of quantum behavior for macroscopic objects. As such, there is a need to provide an optical interferometer that is insensitive to thermal noise. [4] H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951), the entire content of which is incorporated herein by reference.[5] H. B. Callen and R. F. Greene, Phys. Rev. 86,702 (1952), the entire content of which is incorporated herein by reference.[6] R. F. Greene and H. B. Callen, Phys. Rev. 88, 1387 (1952), the entire content of which is incorporated herein by reference.